Analytical model of dynamic crack evolution in tempered and strengthened glass plates

摘要

Modern buildings and vehicles are increasingly employing tempered and strengthened glass plates as architectural and critical load-bearing structural components. Nevertheless, the fracture behavior of these components is only poorly understood and the literature is largely empirical or anecdotal. In this manuscript we implement a semi-static fracture mechanics-based model to describe the evolution of a single crack in tempered and strengthened glass plates. This analytical model applies to cracks driven by residual stress and to fracture origins located at the plate's symmetry plane. The model was validated by comparing the branching length, , and the mirror radius, , computed, to mechanical tests conducted by the authors and results reported in the literature. Branching lengths and mirror radii were found to strongly correlate with the plate's thickness, , and with the peak tensile stress, . It was found that crack branching and mist formation are bounded by the non-dimensional parameter and respectively. Finally, it was determined that the branching length displayed a non-zero lower bound approximately equal to a quarter of the plate's thickness whereas the mirror radius had a theoretical zero lower-bound.